I am using the vegan package in R to do a redundancy analysis (RDA, a part of canonical correlation analysis). My response data is binary and my explanatory variables contains 0, 0.5 an 1. I get quite low eigenvalues (~0.05) and my question is how is the binary data affecting the eigenvalue? Will the variability always be 'badly' explained?
You don't explain if you do some normalization of the variables via scaling them, but it is completely normal to have the canonical variables around the 0.
The variability that they can explain depend on the data itself or the experiment. If the two datasets have low in common the CCA won't be able to explain it, or if it does it will be a false positive.